remaining in a player’s stack (the stacks are reset to a
fixed amount of 200 big blinds at the start of each
hand). Thus, the game tree for no-limit has a much
larger branching factor and is significantly larger;
there are 10165 nodes in the game tree for no-limit,
while there are around 1017 nodes for limit (Johanson
2013). In 2007 a program called Polaris that was created by researchers at the University of Alberta played
four duplicate 500-hand matches against human professionals. The program won one match, tied one,
and lost two, thus losing the match overall. In 2008
an improved version of Polaris competed against six
human professionals in a second match, this time
coming out victorious (three wins, two losses, and
one tie). There have also been highly-publicized
human versus machine competitions for other
games; for example, chess program Deep Blue lost to
human expert Garry Kasparov in 1996 and beat him
in 1997, and Jeopardy! agent Watson defeated human
champions in 2011.

Claudico is Latin for “I limp.” Limping is the nameof a specific play in poker. After the initial antes havebeen paid, the first player to act is the small blind andhe has three available actions; fold (forfeit the pot),call (match the big blind by putting in 50 chipsmore), or raise by putting in additional chips beyondthose needed to call (a raise can be any integralamount from 200 chips up to 20,000 chips in this sit-uation). The second option of just calling is calledlimping and has traditionally been viewed as a veryweak play only made by bad players. In one popularbook on strategy, Phil Gordon writes,Limping is for Losers. This is the most important fun-damental in poker — for every game, for every tour-nament, every stake: If you are the first player to vol-untarily commit chips to the pot, open for a raise.Limping is inevitably a losing play. If you see a personat the table limping, you can be fairly sure he is a badplayer. Bottom line: If your hand is worth playing, it isworth raising (Gordon 2011).

Claudico actually limps close to 10 percent of its
hands, and based on discussion with the human
players who did analysis it seems to have profited
overall from the hands it limped. Claudico also
makes several other plays that challenge conventional human poker strategy; for example it sometimes makes very small bets of 10 percent of the pot,
and sometimes very large all-in bets for many times
the pot (for example, betting 20,000 into a pot of
500). By contrast, human players typically utilize a
small number of bet sizes, usually between half pot
and pot.

Competition DesignTo evaluate the performance, judges used “duplicate”scoring, in which the same hands were played twicewith the cards reversed to reduce the role of luck (andthereby the variance). For example, suppose humanA has pocket aces and the computer has pocket kings,and A wins $5,000. This would indicate that thehuman outplayed the computer. However, supposehuman B has the pocket kings against the computer’spocket aces in the identical situation and the com-puter wins $10,000. Then, taking both of theseresults into account, an improved estimator of per-formance would indicate that the computer out-played the human, after the role of luck in the resultwas significantly reduced. Each human was given apartner, who played the identical hands against Clau-dico with the cards reversed. Polk was paired withLes, and Kim was paired with Li. The players playedin two different rooms of the casino simultaneously,with one player from each of the pairings in eachroom (so that both players in each room had thesame cards, while both players in the other room hadthe cards that Claudico had in the first room).

In total, the humans ended up winning the match
by 732,713 chips, which corresponds to a win rate of
9. 16 big blinds per 100 hands (BB/100), a common
metric used to evaluate performance in poker. (The
small blind (SB) and big blind (BB) correspond to initial investments, or “antes” of the players. In the
match, the SB was 50 chips and the BB was 100
chips.) This was a relatively decisive win for the
humans and was statistically significant at the 90 percent confidence level, though it was not statistically
significant at the 95 percent level. To put these results
into some perspective, Dong Kim won a challenge
match against a strong professional player Nick
Frame by 13. 87 BB/100 (he won by $103,992 over
15,000 hands with blinds SB=$25, BB=$50), and
Doug Polk defeated Ben Sulsky in another high-profile challenge match by 24. 67 BB/100 (he won by
$740,000 over 15,000 hands with blinds SB = $100,
BB = $200).

The chips were just a placeholder to keep track of
the score and did not represent real money; the
humans were paid at the end from a prize pool of
$100,000 which had been donated from Rivers Casino and Microsoft Research. The human with the
smallest profit over the match received $10,000,
while the other humans received $10,000 plus additional payoff in proportion to the profit above the
lowest profit.

Agent ArchitectureClaudico was an improved version of an earlier agentcalled Tartanian7 that came in first place in the 2014AAAI computer poker competition, beating eachopposing agent with statistical significance. Thearchitecture of that agent has been described in detailin a recent paper (Brown, Ganzfried, and Sandholm2015). At a very high level, the design of the agentfollows the three-step procedure depicted in figure 1,which is the leading paradigm used by many of thestrongest agents for large games (that is, games that